Preventing Fatal Gateway Suppression in Condition-Based Maintenance: A Formally Verified Sheaf-Theoretic Approach

(05/09) : Python reproducibility has been added, paper formatting issues have been fixed. This paper has not been published, but has been submitted to Formal Methods in System Design. (05/04) : Lean code has been added and the paper has been updated with new citations. This paper has not been published. Abstract : Condition-based maintenance (CBM) gateways sup-press sensor alarms to prevent false positives from global eventssuch as hard landings and turbulence. Incidents have been reportedwhere this suppression was fatal: a gateway classified a real localmechanical failure as a benign global event because multiple co-located sensors were anomalous—exactly the pattern produced byboth global events and propagating local failures. No existing ap-proach reliably distinguishes the two cases, because all currentmethods classify anomalies by their observed pattern rather thanby the structural role of each sensor in the physical system.We solve this gateway problem by classifying sensors via al-gebraic multigrid (AMG) on a cellular sheaf Laplacian derivedfrom the physical coupling structure. Sensors at flabby positions(C-points) carry recoverable information whose anomalies may besuppressed; sensors at non-flabby positions (F-points) carry uniquestructural data whose anomalies must always escalate. This clas-sification is O(N ) and structurally prevents the fatal suppressionregardless of which or how many neighbouring sensors are alsoanomalous. A Koopman dynamic detection layer catches symmet-ric structural damage invisible to static analysis. All safety claimsare formally verified in Lean 4 with zero sorry across 10 failurescenarios in under 20 seconds.The AMG C/F classification has a deeper mathematical inter-pretation via Jensen’s formula on the Koopman resolvent, connect-ing the gateway problem to the Three Rings spectral certificationframework [17]. The C-points correspond to eigenvalues deep inthe stable region; the F-points to eigenvalues near the stabilityboundary. This connection provides universal failure bounds with-out combinatorial enumeration.